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arXiv · 2304.13384

Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations

Pablo D. Carrasco·Federico Rodriguez-Hertz
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Abstract

In this paper we prove that for topologically mixing metric Anosov flows their equilibrium states corresponding to H\"older potentials satisfy a strong rigidity property: they are determined only by their disintegrations on (strong) stable or unstable leaves. As a consequence we deduce: the corresponding horocyclic foliations of such systems are uniquely quasi-ergodic, provided that the corresponding Jacobian is H\"older, without any restriction on the dimension of the invariant distributions. This gives another proof of a result of Babillott-Ledrappier.

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Pablo D. Carrasco, Federico Rodriguez-Hertz. 2023-04-26. Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations. https://arxiv.org/abs/2304.13384

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